Question

My sister's birthday is in a few weeks and I would like to buy her a vase. The first vase is acylinder with diameter 10 cm and height 40 cm. The second vase is a cone with base diameter 16cm and height 45 cm. The third vase is a sphere with diameter 18 cm. I want to purchase the onethat holds the most water. Which vase should I purchase?

Answer 1

Cylinder Vase

EXPLANATION :

Recall the volume formulas :

`\begin{gathered} \text{ Cylinder :} \\ V=\pi r^2h \\ \\ \text{ Cone :} \\ V=(1)/(3)\pi r^2h \\ \\ \text{ Sphere :} \\ V=(4)/(3)\pi r^3 \end{gathered}`

Solve the volumes of each solid :

Note that the radius is half of the diameter.

`\begin{gathered} \text{ Cylinder with diameter of 10 cm, so r = 5 cm and the height is h = 40 cm :} \\ V=\pi r^2h \\ V=\pi(5)^2(40)=1000\pi cm^3 \\ \\ \text{ Cone with diameter of 16 cm, so r = 8 cm and the height is h = 45 cm :} \\ V=(1)/(3)\pi r^2h \\ V=(1)/(3)\pi(8)^2(45)=960cm^3 \\ \\ \text{ Sphere with diameter of 18 cm, so r = 9 cm :} \\ V=(4)/(3)\pi r^3 \\ V=(4)/(3)\pi(9)^3=972cm^3 \end{gathered}`

The vase that holds the most water is the vase with the largest volume.

And that's Cylinder vase